A localized consensus-based sampling algorithm
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918199815045120 |
|---|---|
| author | Bouillon, Arne Bodard, Alexander Patrinos, Panagiotis Nuyens, Dirk Samaey, Giovanni |
| author_facet | Bouillon, Arne Bodard, Alexander Patrinos, Panagiotis Nuyens, Dirk Samaey, Giovanni |
| contents | We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we approximate the potential with a Moreau envelope, replace the gradient in the Langevin equation with a proximal operator, and finally approximate this operator by a weighted mean. Under Gaussian initial and target distributions, this procedure recovers the standard CBS dynamics. In addition, when we retain only the approximations valid beyond the Gaussian case, we retrieve a refined variant of polarized CBS. The resulting algorithm, which we call localized consensus-based sampling, is affine-invariant, exact for Gaussian targets in the mean-field limit, and demonstrates improved robustness over polarized CBS in numerical experiments. Like other consensus-based methods, localized CBS is fully gradient-free and easily parallelizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A localized consensus-based sampling algorithm Bouillon, Arne Bodard, Alexander Patrinos, Panagiotis Nuyens, Dirk Samaey, Giovanni Numerical Analysis Optimization and Control 62F15 (Primary) 65C05, 65C35, 82C31 (Secondary) We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we approximate the potential with a Moreau envelope, replace the gradient in the Langevin equation with a proximal operator, and finally approximate this operator by a weighted mean. Under Gaussian initial and target distributions, this procedure recovers the standard CBS dynamics. In addition, when we retain only the approximations valid beyond the Gaussian case, we retrieve a refined variant of polarized CBS. The resulting algorithm, which we call localized consensus-based sampling, is affine-invariant, exact for Gaussian targets in the mean-field limit, and demonstrates improved robustness over polarized CBS in numerical experiments. Like other consensus-based methods, localized CBS is fully gradient-free and easily parallelizable. |
| title | A localized consensus-based sampling algorithm |
| topic | Numerical Analysis Optimization and Control 62F15 (Primary) 65C05, 65C35, 82C31 (Secondary) |
| url | https://arxiv.org/abs/2505.24861 |